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RMS Speed Formula

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The Root Mean Square Velocity is the square root of the average of the square of the velocity. As such, it has units of velocity. Check FAQs

V rms = \sqrt{\frac{3 \cdot [R] \cdot T g}{M molar}}

V_rms - Root Mean Square Velocity?T_g - Temperature of Gas?M_molar - Molar Mass?[R] - Universal gas constant?

RMS Speed Example

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Here is how the RMS Speed equation looks like with Values.

Here is how the RMS Speed equation looks like with Units.

Here is how the RMS Speed equation looks like.

159.7012 = \sqrt{\frac{3 \cdot 8.3145 \cdot 45}{44.01}}

159.7012m/s = \sqrt{\frac{3 \cdot 8.3145 \cdot 45K}{44.01g/mol}}

159.7012 = \sqrt{\frac{3 \cdot 8.3145 \cdot 45}{44.01}}

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RMS Speed Solution

Follow our step by step solution on how to calculate RMS Speed?

FIRST Step Consider the formula

V rms = \sqrt{\frac{3 \cdot [R] \cdot T g}{M molar}}

Next Step Substitute values of Variables

∴

V rms = \sqrt{\frac{3 \cdot [R] \cdot 45K}{44.01g/mol}}

Next Step Substitute values of Constants

∴

V rms = \sqrt{\frac{3 \cdot 8.3145 \cdot 45K}{44.01g/mol}}

Next Step Convert Units

∴

V rms = \sqrt{\frac{3 \cdot 8.3145 \cdot 45K}{0.044kg/mol}}

Next Step Prepare to Evaluate

∴

V rms = \sqrt{\frac{3 \cdot 8.3145 \cdot 45}{0.044}}

Next Step Evaluate

∴

V rms = 159.701241569226m/s

LAST Step Rounding Answer

∴

V rms = 159.7012m/s

RMS Speed Formula Elements

Variables

Constants

Functions

Root Mean Square Velocity

The Root Mean Square Velocity is the square root of the average of the square of the velocity. As such, it has units of velocity.

Symbol: V_rms

Measurement: SpeedUnit: m/s

Note: Value can be positive or negative.

Formulas to find Root Mean Square Velocity

Temperature of Gas

The temperature of Gas is the measure of hotness or coldness of a gas.

Symbol: T_g

Measurement: TemperatureUnit: K

Note: Value can be positive or negative.

Formulas to find Temperature of Gas

Molar Mass

Molar Mass is the mass of a given substance divided by the amount of substance.

Symbol: M_molar

Measurement: Molar MassUnit: g/mol

Note: Value can be positive or negative.

Formulas to find Molar Mass

Universal gas constant

Universal gas constant is a fundamental physical constant that appears in the ideal gas law, relating the pressure, volume, and temperature of an ideal gas.

Symbol: [R]

Value: 8.31446261815324

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Factors of Thermodynamics category

Go Absolute Humidity

AH = \frac{W}{V}

Go Average Speed of Gases

V avg = \sqrt{\frac{8 \cdot [R] \cdot T ga}{π \cdot M molar}}

Go Degree of Freedom given Equipartition Energy

F = 2 \cdot \frac{K}{[BoltZ] \cdot T gb}

Go Molar Mass of Gas given Average Speed of Gas

M molar = \frac{8 \cdot [R] \cdot T ga}{π \cdot {V avg}^{2}}

How to Evaluate RMS Speed?

RMS Speed evaluator uses Root Mean Square Velocity = sqrt((3*[R]*Temperature of Gas)/Molar Mass) to evaluate the Root Mean Square Velocity, RMS Speed formula is defined as a measure of the average speed of particles in a gas, reflecting their kinetic energy and temperature. It provides insight into the behavior of gas molecules under varying thermal conditions. Root Mean Square Velocity is denoted by V_rms symbol.

How to evaluate RMS Speed using this online evaluator? To use this online evaluator for RMS Speed, enter Temperature of Gas (T_g) & Molar Mass (M_molar) and hit the calculate button.

FAQs on RMS Speed

What is the formula to find RMS Speed?

The formula of RMS Speed is expressed as Root Mean Square Velocity = sqrt((3*[R]*Temperature of Gas)/Molar Mass). Here is an example- 159.8786 = sqrt((3*[R]*45.1)/0.04401).

How to calculate RMS Speed?

With Temperature of Gas (T_g) & Molar Mass (M_molar) we can find RMS Speed using the formula - Root Mean Square Velocity = sqrt((3*[R]*Temperature of Gas)/Molar Mass). This formula also uses Universal gas constant and Square Root (sqrt) function(s).

Can the RMS Speed be negative?

Yes, the RMS Speed, measured in Speed can be negative.

Which unit is used to measure RMS Speed?

RMS Speed is usually measured using the Meter per Second[m/s] for Speed. Meter per Minute[m/s], Meter per Hour[m/s], Kilometer per Hour[m/s] are the few other units in which RMS Speed can be measured.

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RMS Speed Formula

RMS Speed Example

RMS Speed Solution

RMS Speed Formula Elements

Other formulas in Factors of Thermodynamics category

How to Evaluate RMS Speed?

FAQs on RMS Speed

Variable Name